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Finite automata capturing winning sequences for all possible variants of the PQ penny flip game

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Figure

Table 1. Correspondence between the operators I, F and H and the letters of the alphabet Σ = {i, f, h}.
Figure 1. This two state automaton APQ captures the moves of the PQ game.
Figure 2. The four-state automaton APQπ/2 captures the possible moves of the PQπ/2 game, in whichthe initial state of the coin is |tails⟩
Figure 3. The automaton APQ6 corresponding to the 6-round PQ6 game.
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